Junior Math Days 2023

Dec 4, 2023, 9:00 AM → Dec 6, 2023, 5:00 PM Europe/Rome

004 (ground floor) and Meeting Room (7th floor) (SISSA)

Valentina Bais (SISSA), Andrea Rosana (Scuola Internazionale Superiore di Studi Avanzati (SISSA)), Lorenzo Sillari (SISSA), Elisa Vitale (SISSA)

Junior Math Days is an event where Master’s students can learn about the mathematical research environment and the life of PhD students at SISSA. 

 

The 2023 edition will take place on 4-5-6 December 2023. 

 

Selected participants can spend three days in the stimulating environment of SISSA and take part in several planned activities. The program includes:

• introductory talks given by professors and post-docs about their research topics: from Mathematical Analysis to Geometry, Mathematical Physics and Applied Mathematics. 
• informal meetings with SISSA students to learn about their work and personal experience at SISSA.

Other activities to experience life in Trieste include:

• a welcome dinner on 3^rd December
• a visit to the city on 5^th December

The schedule of the event is available in the Timetable section. The list of speakers and titles of their talks will be updated soon.

 

Please read the How to apply section before registering to the event. 

For further information, feel free to send us an email at jmd.sissa (‘at’) gmail.com.

 

This event is sponsored by SISSA Mathematics Area and Comitato Unico di Garanzia (CUG).

JMD2023 poster.pdf

Monday, December 4

9:15 AM → 10:15 AM Introduction to optimal transport

Speaker: Prof. Nicola Gigli

Nicola Gigli - Introduction to optimal transport.pdf

10:15 AM → 11:10 AM Counting curves: which, how and why

Speaker: Prof. Barbara Fantechi

Barbara Fantechi - Counting curves: which, how and why.pdf

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM Title TBA

Speaker: Prof. Andrea Cangiani

12:40 PM → 1:35 PM Geometry and Control

Control system is a family of dynamical systems acting on the same state space. The systems in the family do not commute and a clever strategy of switching between them allows to build a desired complicated dynamics from simple blocks. Transformation groups and geometry play a crucial role.
We'll start from simple kinematic models, then discuss universal controllability properties and nice geometric optimal control problems.
This is an expository talk, no particular prerequisites are required.

Speaker: Prof. Andrei Agrachev

Andrei Agrachev - Geometry and control.pdf

1:35 PM → 3:00 PM Lunch break

3:00 PM → 4:15 PM Meeting with PhD students

4:15 PM → 4:45 PM Coffee break

4:45 PM → 6:00 PM Meeting with PhD students

Tuesday, December 5

9:15 AM → 10:15 AM Integrable systems: a bird's-eye view

The notion of finite dimensional integrable systems in analytical mechanics was well established in the XIX Century. New non-linear equations appeared in applications to mathematical physics in the XX Century, which turned out to be analytically treatable and integrable. I will give an introduction to infinite dimensional integrable systems and Lax Pairs, using the KdV equation as an example.

Speaker: Prof. Davide Guzzetti

Davide Guzzetti - Integrable Systems. A bird's eye view.pdf

10:15 AM → 11:10 AM Complex differential geometry

Speaker: Prof. Jacopo Stoppa

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM Reduced-Order Models: Fundamentals and Applications

Speaker: Prof. Gianluigi Rozza

Gianluigi Rozza - Reduced-order models. Fundamentals and applications.pdf

12:40 PM → 1:35 PM Convex bodies and algebraic geometry

In this seminar I will discuss some interesting and unexpected connections between the problem of counting the number of solutions to a system of algebraic equations and computing the volume of a certain convex body associated to the system -- magically they turn out to be essentially the same problem!

Speaker: Prof. Antonio Lerario

1:35 PM → 3:00 PM Lunch break

3:00 PM → 4:15 PM Meeting with PhD students

4:15 PM → 4:45 PM Coffee break

4:45 PM → 6:00 PM Meeting with PhD students

Wednesday, December 6

9:15 AM → 10:15 AM Groups and manifolds: a sample of low-dimensional topology

A presentation of a group can be encoded into a link, i.e., a disjoint union of knots in the three-dimensional sphere. Such link contains enough information to (de)construct a four-dimensional smooth manifold. We'll sample this algorithm and give an overview of a proof of the following result.

Theorem (Dehn): Any finitely presented group is realised as the fundamental group of a closed smooth orientable 4-manifold.

Speaker: Prof. Rafael Torres

10:15 AM → 11:10 AM Universality in Condensed Matter and Statistical Mathematical Physics

Universality is a central concept in modern physics, and the rigorous derivation of such a property is an important challenge for mathematical physics. In this field, universality refers to the fact that a certain number of macroscopic properties close to phase transition are independent from microscopic details of the model (that are called irrelevant). A natural setting to investigate such property is when a certain model is perturbed and then one aims to understand the class of irrelevant perturbations for which universality holds and the class of relevant ones for which it is lost. In this presentation I will describe the physical motivation, the mathematical setting and provide a couple of results obtained recently.

Speaker: Dr Matteo Gallone

11:10 AM → 11:40 AM Coffee break

11:40 AM → 12:40 PM An introduction to neural networks from the mathematical point of view

Speaker: Prof. Sebastian Goldt

Sebastian Goldt - An introduction to neural networks.pdf

12:40 PM → 1:35 PM Meeting with PhD students

1:35 PM → 3:00 PM Lunch break